NAG Library Routine Document
M01ZCF decomposes a permutation into cycles, as an aid to reordering ranked data.
||IPERM(M2), M1, M2, ICYCL(M2), IFAIL
M01ZCF is provided as an aid to reordering arbitrary data structures without using additional storage. However, you should consider carefully whether it is necessary to rearrange yourr data, or whether it would be simpler and more efficient to refer to the data in sorted order using an index vector, or to create a copy of the data in sorted order.
To rearrange data into a different order without using additional storage, the simplest method is to decompose the permutation which specifies the new order into cycles and then to do a cyclic permutation of the data items in each cycle. (This is the method used by the M01E reordering routines.) Given a vector IRANK which specifies the ranks of the data (as generated by the M01D routines), M01ZCF generates a new vector ICYCL
, in which the permutation is represented in its component cycles, with the first element of each cycle negated. For example, the permutation
is composed of the cycles
and the vector ICYCL
generated by M01ZCF contains
In order to rearrange the data according to the specified ranks:
- item must be left in place;
- items and must be interchanged;
- items , , and must be moved right one place round the cycle.
The complete rearrangement can be achieved by the following code:
DO 10 K = M1, M2
I = ICYCL(K)
IF (I.LT.0) THEN
J = -I
[swap items I and J]
- 1: IPERM(M2) – INTEGER arrayInput/Output
: elements M1
must contain a permutation of the integers M1
On exit: is used as internal workpsace prior to being restored and hence is unchanged.
- 2: M1 – INTEGERInput
- 3: M2 – INTEGERInput
must specify the range of elements used in the array IPERM
and the range of values in the permutation, as specified under IPERM
- 4: ICYCL(M2) – INTEGER arrayOutput
: elements M1
contain a representation of the permutation as a list of cycles, with the first integer in each cycle negated. (See Section 3
- 5: IFAIL – INTEGERInput/Output
must be set to
. If you are unfamiliar with this parameter you should refer to Section 3.3
in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value
is recommended. If the output of error messages is undesirable, then the value
is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is
. When the value is used it is essential to test the value of IFAIL on exit.
unless the routine detects an error or a warning has been flagged (see Section 6
6 Error Indicators and Warnings
If on entry
, explanatory error messages are output on the current error message unit (as defined by X04AAF
Errors or warnings detected by the routine:
contain a value outside the range M1
contain a repeated value.
, elements M1
do not contain a permutation of the integers M1
This example reads a matrix of real numbers and rearranges its columns so that the elements of the
th row are in ascending order. To do this, the program first calls M01DJF
to rank the elements of the
th row, and then calls M01ZCF to decompose the rank vector into cycles. It then rearranges the columns using the framework of code suggested in Section 3
. The value of
is read from the data file.
9.1 Program Text
Program Text (m01zcfe.f90)
9.2 Program Data
Program Data (m01zcfe.d)
9.3 Program Results
Program Results (m01zcfe.r)